"Forms" Can I use a drop down field to direct the form information to a specific email address?

Christopher,

The form details go directly into a new row in your sheet, either top or bottom as configured under the form options. Once it is in the form, you could redirect the information via a reminder.

Unfortunately, a contact column does not support formulas.

I would have used a formula and the Autofill feature (which works from Webforms) if it did. 

How many countries and how many emails are needed?

If there are not many, you could set up a form for each, with the difference being the default value for the contact column (which could be hidden from the form's end user).

A notification could then be set up to trigger when the information is added and go to the person in the contact column.

Alternatively, there are third party software such as Azuqua that monitor Smartsheets and take action based on what has occurred. I believe there are others besides Azuqua but I have not tested them yet.

Even more alternatively, you could have the info go to a single email address and use the email programs to parse and redirect the email to its correct reciepient. This feels like a hack, but could be simple to set up.

Or maybe I missed an obvious solution. 

Hope this helps.

Craig

Azuqua is a great option for this! I also recommend Zapier which can do this as well, but has a free version of their app (Azuqua is paid only).